Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

Jiayun Chen; Qiye Zhang; Deren Han; Jiaxin Xie

Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

Numerical Analysis 2026-08-02 v1

Authors: Jiayun Chen , Qiye Zhang , Deren Han , Jiaxin Xie

Abstract

In this paper, we systematically incorporate the Polyak step-size into the randomized iterative method to improve its efficiency for solving generalized absolute value equations. In particular, we adopt the Polyak step-size within a stochastic iterative setting where the objective function updates dynamically at every step, unlike the classical Polyak step-size designed for deterministic optimization with fixed objective functions. Consequently, this novel implementation differs from the conventional Polyak scheme and demands a dedicated convergence analysis. We rigorously analyze the convergence properties of the proposed method and establish its linear convergence in expectation. Numerical experiments demonstrate that the incorporation of the Polyak step-size substantially improves the computational performance of randomized iterative methods with constant step-sizes.

Cite

@article{arxiv.2608.00952,
  title  = {Randomized iterative methods with Polyak step-size for solving generalized absolute value equations},
  author = {Jiayun Chen and Qiye Zhang and Deren Han and Jiaxin Xie},
  journal= {arXiv preprint arXiv:2608.00952},
  year   = {2026}
}